PTQ

In the fig. two circles intersect each other in point A and B. Secants through the point A intersect the circles in point P,Q and R,S. Line PR and SQ intersect in T. (i) PTQ and PBQ are supplementary. (ii) square BSTR is cyclic quadrilateral.

P is a point on the parabola y^(2)=4ax whose ordinate is equal to its abscissa and PQ is focal chord, R and S are the feet of the perpendiculars from P and Q respectively on the tangent at the vertex, T is the foot of the perpendicular from Q to PR, area of the triangle PTQ is